Finite Group Databasebeta

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C3×C43×D145 #49153453

order37410
automorphism?
homologyAbelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C1

Aliases

direct productC3×C43×D145
unambiguous semidirect productC5⋊(C3×C43×D29)
unambiguous semidirect productC29⋊(C3×D5×C43)

Splittings

Fitting, socle, HallC3×C5×C29×C43 ⋊ C2
derived, HallC5×C29 ⋊ C2×C3×C43
HallC5×C29×C43 ⋊ C2×C3
HallC3×C29×C43 ⋊ D5
HallC29×C43 ⋊ C3×D5
HallC3×C5×C43 ⋊ D29
HallC3×C5×C29 ⋊ C2×C43
HallC5×C43 ⋊ C3×D29
HallC3×C29 ⋊ D5×C43
SylowC29 ⋊ C3×D5×C43
HallC3×C5 ⋊ C43×D29
SylowC5 ⋊ C3×C43×D29

Subgroups

subgroupG/H
center, hypercenterC3×C43D145
commutator, cosocle, hypocenterC5×C29C2×C3×C43
FrattiniC1G
Fitting, socleC3×C5×C29×C43C2
LCSG ▷ C5×C29
UCSC1 ◁ C3×C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18705

Conjugacy classes & character table

9546 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37410, 8);